Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#901 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 3. #11720887 | C2 | semidirect |
| 5. #11720535 | C2 | semidirect |
| 6. #11720289 | C2 | semidirect |
| 7. #11720287 | C2 | semidirect |
| 35. C2×#3664 | D3 | semidirect |
| 106. #901 | D9 | semidirect |
| 215. C3×C9 | #471 | semidirect |
| 299. C9 | #5177 | semidirect |
| 335. C3 | #10588822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#901 | 2 |
| C2×C3×#3664 | 2 |
| #11720887 | 2 |
| #11720882 | 2 |
| #11720535 | 2 |
| #11720289 | 2 |
| #11720287 | 2 |
| #10590925 | 3 |
| #10588822 | 3 |